Berezansky et al. 2010 proposed an open problem: How are the dynamic behaviors of the well-known Nicholson’s blowflies model with a delayed linear harvesting. In this paper, we mainly study the existence of Hopf bifurcation of Nicholson’s blowflies model with a delayed linear harvesting. To that end, the stability and Hopf bifurcation of a general functional differential equation with two dependent delays are investigated. We show that if the difference between the two dependent delays is constant, by using one of the delays as a bifurcation parameter, sufficient conditions of stability and Hopf bifurcation are obtained. In addition, in order to determine the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, explicit formulas are given by using the normal form theory. The main results can be applied to guarantee the existence of Hopf bifurcation in Nicholson’s blowflies model with a delayed linear harvesting. Our research partially answers the open problem proposed by Berezansky et al. 2010.
Chen et al. (Fri,) studied this question.